Place a large pot/dutch oven over medium heat. Add the olive oil, onions, carrots and a generous pinch of salt and sauté for 7-10 minutes.
Stir in the potatoes, corn, vegetable broth, nutritional yeast, salt, pepper, garlic powder, and smoked paprika. Cover and bring to boil.
Once boiling, reduce heat to low and simmer for 30 minutes with the cover on.
OPTIONAL: if making the roasted broccoli, prepare this now. Preheat oven to 400F. Line a baking sheet with parchment paper. Toss the broccoli florets with olive oil, salt & pepper and add to the baking sheet. Roast for 15-20 minutes.
Add the white beans and non-dairy milk to a blender along with about 3/4 of the soup. Blend until creamy.
Pour the mixture back into the pot and stir to combine. Taste and adjust the soup for seasoning. I like to serve it topped with roasted broccoli.